The present invention relates to polarimeters and, more specifically, to polarimeters based on liquid crystal variable retarders for determining the state of polarization of light incident thereon.
In applications ranging from astronomy to telecommunications, it is often desired to have knowledge of the state of polarization (SOP) of light. For example, astronomical applications include the utilization of polarization information of light received at a telescope as a tool for mapping solar magnetic fields. Chemical and pharmaceutical industries exploit the effect of enantiomerically enriched chiral compounds on the state of polarization for light passed through such compounds, i.e. optical activity. The state of polarization plays a significant role in telecommunications since polarization mode dispersion and polarization-dependent loss present considerable impediments to increased optical bandwidth. Furthermore, polarimetric measurements are used in a wide array of materials characterization, such as in quantification of thin film thickness and index and as a tool for mapping internal material strain via stress-induced birefringence.
The art and science of polarimetry is vast with a history that extends well over a century, and, accordingly, various mathematical descriptions of polarized light have long been established. For example, in the Stokes vector representation, the full SOP is characterized as a four element Stokes vector {overscore (S)}, which is defined as                               S          _                ≡                  (                                                                      S                  0                                                                                                      S                  1                                                                                                      S                  2                                                                                                      S                  3                                                              )                                    (        1        )            
where
S0=Total light intensity,
S1=Intensity difference between horizontal and vertical linearly polarized components,
S2=Intensity difference between xc2x145xc2x0 linearly polarized components and
S3=Intensity difference between right and left circularly polarized components
Other important and often utilized polarization parameters, such as the degree of polarization (DOP), degree of linear polarization (DOLP), degree of circular polarization (DOCP), ellipticity and orientation of major axis, are directly obtainable from the Stokes vector components. For example,                     DOP        =                                                            S                1                2                            +                              S                2                2                            -                              S                3                2                                                          S            0                                              (        2        )                                DOLP        =                                                            S                1                2                            +                              S                2                2                                                          S            0                                              (        3        )                                DOCP        =                              S            3                                S            0                                              (        4        )            
Turning now to the drawings, wherein like components are indicated by like reference numbers throughout the various figures where possible, attention is immediately directed to FIG. 1, which illustrates a Poincarxc3xa9 sphere 10. The Pioncarxc3xa9 sphere is a commonly used graphical visualization aid for the SOP. As shown in FIG. 1, a Poincarxc3xa9 sphere 10 represents a mapping of all possible SOPs onto the surface of a sphere. A north pole 12 and a south pole 14 of Poincarxc3xa9 sphere 10 correspond to right and left circularly polarized light, respectively. An equator 15 corresponds to linearly polarized light. Arbitrarily chosen opposing points 16 and 18 along the equator represent horizontal and vertical linear polarizations, and opposing points 20 and 22, which define a line orthogonal to the line defined by points 16 and 18, represent +45xc2x0 and xe2x88x9245xc2x0 linear polarizations, respectively. In terms of the Stokes vector of Eq. (1), the bottom three components of the Stokes vector define a three-dimensional vector that points from the center of the Poincarxc3xa9 sphere to a point on the surface of the sphere.
A Stokes polarimeter is a device for determining the SOP of light incident thereon by measuring the components of the Stokes vector of Eq. (1). In terms of the Poincarxc3xa9 sphere, the Stokes polarimeter determines the components of the Stokes vector by measuring the projections along the orthogonal axes of the Poincarxc3xa9 sphere. For example, passing the light through a horizontal linear polarizer is equivalent to measuring the projection of the Stokes vector along the horizontal axis. As another example, for measurements of circular polarization components, a quarterwave plate can be utilized to convert circular polarization components into a linear polarization, from which a linear polarizer may then be used to determine the projection. In general, multiple measurements must be made in order to obtain all four components of the Stokes vector.
Currently available polarimeter technologies use polarization optics to extract the polarization information of input light, which is received at one or more detectors and converted to electrical signals. There are mainly four types of existing polarimeters, the basic configurations of which are illustrated in FIGS. 2A-2D.
FIG. 2A illustrates a manually operated polarimeter 30 including an optical assembly 32 and a detector 39. Optical assembly 32 includes a casing 33, which contains passive optical elements (not shown) such as a polarizing element and an optical retarder. Casing 33 includes an opening 35 for accepting an input light 37 such that input light 37 is acted upon by the polarizing element and the optical retarder within optical assembly 32, and at least a portion of input light 37 is transmitted through optical assembly 32 to be detected by a detector 38. During normal operation, the user of polarimeter 30 manually rotates and flips optical assembly 32 to obtain data at detector 38. Optical assembly 32 is usually configured to have at least four measurement positions, and the data obtained at detector 38 is analyzed by a computer 39 to convert the four measurements into Stokes parameters. A device based on the design as shown in FIG. 2A is available from Optics for Research, for example, and such a design has been described in the literature.1 A manually operated polarimeter such as polarimeter 30 is limited in that a relatively long time (i.e., several seconds) is required to take the full set of measurements. As a result, the calculated parameters are susceptible to inaccuracies due to power and polarization fluctuations in the input light. Also, since passive, static optical elements are used in the optical assembly, the wavelength range is limited due to the effective range of the optical elements.
Another prior art polarimeter is shown in FIG. 2B. A polarimeter 40 of FIG. 2B is a xe2x80x9cdivision of aperturexe2x80x9d or xe2x80x9cdivision of amplitudexe2x80x9d type polarimeter. Polarimeter 40 includes a beam expander 42, a collimator 43, a Stokes filter array 45, which includes at least four filters 46, and a detector array 47, in which a plurality of detectors 48 are aranged to detect light transmitted through each of filters 46. Input light 37 is expanded by beam expander 42 then collimated by collimator 43 to be incident on Stokes filter array 45. Each filter 46 is configured to be preferentially sensitive to different polarizations such that at least four simultaneous measurements may be taken to obtain the complete Stokes vector. Polarimeters based on the design shown in FIG. 2B are commercially available from companies such as A flash Corporation, Gaertner Scientific, Santec and General Photonics. Various modifications of polarimeter 40 are disclosed in the literature, such as the xe2x80x9cphotopolarimeterxe2x80x9d which uses non-normal illumination of four detectors arranged in a non-planar configuration.2 Polarimeter 40 is advantageous in comparison to polarimeter 30 of FIG. 2A due to the high speed in which data may be acquired, limited only by the detector speed. However, polarimeter 40 is still limited in the useful wavelength range due to the wavelength-dependence of the Stokes filters, and the need for a plurality of balanced detectors adds to the total cost of the system. Also, polarimeter 40 is extremely sensitive to the angle of incidence of the input light. In order to overcome this incidence angle sensitivity, other researchers have suggested various configurations in which light propagation into the polarimeter is confined by the use of optical fibers.3-9 Yet, the use of fibers adds to the complexity and cost of the polarimeter while further limiting useful optical bandwidth, and therefore is not desirable in many applications.
A third type of polarimeter is shown in FIG. 2C. A polarimeter 50 includes first and second spinning retarders 52A and 52B, respectively, which spin in a direction indicated by curved arrows 53. Polarimeter 50 further includes an analyzer 54 and a detector 56. First and second spinning retarders 52A and 52B are configured to spin at different rate such that they modulate input light 37 at different rates, and detector 56 is configured to cooperate with first and second spinning retarders 52A and 52B to detect and demodulate the light received thereon by lock-in detection. The specific rate of spin, as well as the retardance values of the spinning retarders, are flexible, although certain retardance values will not work in the system (e.g., a one-wave retarder). Such polarimeters are commercially available from, for example, Thor Labs and are disclosed in a number of patents.10-11 Tremendous accuracy ( less than 0.001% error) has been achieved using the design shown in FIG. 2C.12 This approach can be advantageous over the polarimeter design shown in FIG. 2A because the duty cycle for measurements is 100% (i.e., data is not just taken at four discrete steps but continuously while the retarders are spinning) and advantageous over both implementations shown in FIGS. 2A and 2B because rapid spin rates, coupled with lock-in detection, limit measurement bandwidth and transfer detection frequencies well above 1/f and other low frequency noise sources. Furthermore, polarimeter 50 requires only a single detector, which can lead to both cost savings and decreased angle of incidence sensitivity over multiple detector designs. However, the polarimeter design of FIG. 2C requires motors to spin the retarders, and the utilizable optical bandwidth is still limited due to the fixed retardance values of the spinning retarders.
A fourth type of polarimeter, as shown in FIG. 2D, is similar in configuration to polarimeter 50 as shown in FIG. 2C but the spinning passive retarders are replaced by stationary active or variable retarders. A polarimeter 60 includes first and second variable retarders 62A and 62B, respectively, with the orientation of optic axes of the two retarders being held fixed (thereby eliminating the need for motors or moving parts) while the retardance values of the two variable retarders are either switched between sets of specific, predetermined values, or rapidly modulated at different rates for the two different retarders.
In the case where the variable retarders are switched between specific, predetermined values, the retardance values of first and second variable retarders 62A and 62B are set to the predetermined values in a discrete, stepwise fashion, and an intensity measurement is taken at each of the predetermined values. The Stokes vector components are calculated based on the measurements taken at detector 56 at the predetermined values. One example of such a polarimeter based on the configuration shown in FIG. 2D and the step-wise measurement scheme is the LC Stokes polarimeter of Meadowlark Optics.13 The LC Stokes polarimeter is configured to take a set of discrete measurements with the variable retarders set at discrete, predetermined retardance values in order to calculate the Stokes vector.
Continuing to refer to FIG. 2D in conjunction with FIG. 2C, polarimeter 60 has the added advantage of wavelength versatility since the retardance values of the variable retarders are not fixed and no moving parts are required, thereby simplifying the system design. The orientations of optical axes, represented by arrows 63A and 63B, of first and second variable retarders 62A and 62B, respectively, are typically chosen such that, for instance, optical axis 63A is vertical while optical axis 63B is positioned at an angle 65 away from the vertical. Small variations in angle 65 are usually accounted for in calibration process.
Referring now to FIG. 2E in conjunction with FIG. 2D, an example of a retardance value schematic for a stepwise polarimeter 50 is illustrated. This example is based on a prior publication regarding the LC Stokes polarimeter published by Meadowlark Optics.13 A graph 70 of FIG. 2E includes a vertical axis 71 representing retardance (in units of waves xcex) and a horizontal axis 72 representing time (in arbitrary units). A first, solid line 73 shows the retardance value settings of first variable retarder 62A, and a second, dashed line 75 shows the retardance value settings of second variable retarder 62B. Times T1-T6 are times at which measurements are taken in order to generate the data for extraction of the Stokes parameters. As shown in graph 70, first variable retarder 62A is first set to a retardance value of zero waves for the measurements taken at times T1-T4, then later held at a retardance value of xcex/4 for the measurements taken at times T5 and T6. Second variable retarder 62B begins at zero wave retardance for time T1, then is switched to a retardance value of xcex/2 for a measurement at time T2. Second variable retarder 62B is reset to a retardance value of xcex/4 for a measurement at time T3, and the second variable retarder is twice switched between retardance values of xcex/4 and 3xcex/4 for measurements at times T3-T6. In this way, the first Stokes parameter S0 of Eq. (1) is determined from any one set of two measurements (T1 and T2, T3 and T4, or T5 and T6), the S1 component is found by comparing the detector readings obtained at times T1 and T2, the S3-component is calculated by using the detector readings obtained at times T3 and T4, and the S2 component is obtained by using the detector readings at times T5 and T6. In other words, the retardance values of the first and second variable retarders are set to predetermined values in a stepwise fashion, with discrete measurements being taken when the first and second variable retarders are fixed at predetermined retardance values for extraction of the Stokes parameters.
Although the Meadowlark LC Stokes polarimeter is sufficient for most applications, this device does have one disadvantage by a relatively slow acquisition time ( greater than hundreds of milliseconds) due to the response times of the LC material and, since only single, discrete measurement are made, also a small measurement duty cycle. Also, it is not trivial to set the retardance values of the LC variable retarder at the exact, discrete values required for the step-wise Stokes parameter measurements.
As an alternative to the scheme shown in FIG. 2E, the retardance values of the two retarders of FIG. 2D may be rapidly oscillated such that the portion of input light 37 transmitted through first and second variable retarders 62A and 62B and analyzer 54 is detected at detector 56 by lock-in detection. The first and second variable retarders are modulated at first and second known frequencies, respectively, such that the polarization information of the input light can be obtained by analysis of the signal detected at the lock-in detector at the first and second known frequencies and their harmonics (usually twice the first and second known frequencies). The first and second variable retarders generally must be driven at different frequencies such that the resulting signals detected at the lock-in detector can be distinguished as being the result of the modulation by the first variable retarder or the second variable retarder. This scheme is analogous to the spinning waveplate technique, except with stationary variable retarders, the retardance of which are oscillated at predetermined frequencies. Various electro-optic and photoelastic materials may be used as the variable retarders. 14-16 For example, KDP or other electro-optic crystalline material is appropriate for use as the variable retarder in this scheme. Alternatively, piezo-electric elements can be used to stress optical fiber or a variety of bulk materials with sufficiently large stress-optical coefficients, such as calcium fluoride, lithium fluoride, or fused silica to induce birefringence. When driven at a resonant frequency, such photo-elastic modulators can obtain sufficient stroke for polarimetry applications. While both crystalline electro-optic and photo-elastic variable retarders are attractive due to their high modulation frequencies, they are expensive and require high voltage driving electronics as well as complex lock-in amplification and/or detection schemes. Liquid crystal materials may provide cost savings and simplified, low-voltage drive electronics, but are traditionally slow in comparison to KDP and electro-optic materials, therefore liquid crystals are generally not suited for use in the retardance oscillation polarimeters.
A sample measuring polarimeter generally measures the SOP of light that has been transmitted through or reflected from a sample. Numerous examples of sample measuring polarimeters exist in the literature. For instance, Oldenbourg et al. disclose a step-wise algorithm for obtaining polarization information from a sample using a polarized microscope including LC variable retarders.17 The algorithm of Oldenbourg et al. sets the LC variable retarders at predetermined, discrete settings by applying a set of predetermined voltage values to the LC variable retarders. Intensity measurements of light transmitted through the LC variable retarders and the sample are taken at a detector, such as a CCD array. Then, the intensity values measured at the predetermined, discrete retardance values are inserted into an algorithm to calculate the retardance values at different portions of the sample. For example, the LC variable retarder of Oldenbourg et al. must be set to four different sets of applied voltages, and thereby retardance value, combinations in order to measure the retardance values of the sample specimen. It is noted that Oldenbourg et al. does not disclose or suggest in any way the measurement or calculation of Stokes parameters. Also, the disclosure of Oldenbourg et al. is limited to applications in a polarized light microscope.
The present invention provides a polarimeter and associated method which serves to reduce or eliminate the foregoing problems in a highly advantageous and heretofore unseen way and which provides still further advantages.
As will be disclosed in more detail hereinafter, there is disclosed herein a method for use in a polarimeter for analyzing a state of polarization of a light beam incident thereon. The polarimeter includes first and second variable retarders and a detector arrangement, wherein the first and second variable retarders are configured to exhibit first and second retardance values, respectively, which first and second retardance values are variable over an overall retardance range. The method includes the steps of directing the light beam through the first and second variable retarders, and sweeping a selected one of the first and second retardance values progressively and unidirectionally through at least a part of the overall retardance range. The method further includes the steps of, for a plurality of retardance values that are produced as the selected one of the first and second retardance values is progressively and unidirectionally swept through the part of the overall retardance range, detecting at the detector arrangement at least a spatial portion of the light beam, and extracting the state of polarization based on the spatial portion of the light beam detected at the detector arrangement corresponding to the plurality of retardance values.
In another aspect of the invention, there is disclosed a method for use in a polarimeter for analyzing a state of polarization of a light beam incident thereon. The polarimeter includes first and second liquid crystal variable retarders, a detector arrangement and a control arrangement, wherein the first and second liquid crystal variable retarders are configured to exhibit first and second retardance values, respectively, which first and second retardance values are variable over an overall retardance range. The control arrangement is configured to supply first and second voltage signals to the first and second liquid crystal variable retarders, respectively, so as to vary at least one of the first and second retardance values. The method includes the steps of directing the light beam through the first and second variable retarders, for a selected one of the first and second voltage signals, using the control arrangement, applying an initial voltage value so as to produce a particular condition at a corresponding one of the first and second liquid crystal variable retarders, and, once the particular condition is achieved, applying a different voltage value as the selected one of the first and second voltage signals for a given time period such that the corresponding one of the first and second retardance values varies progressively and unidirectionally during the given time period. The method further includes the steps of, during the given time period, detecting at the detector arrangement at least a spatial portion of the light beam responsive to the changing retardance, and extracting the state of polarization based on the spatial portion of the light beam detected at the detector arrangement.
In yet another aspect of the invention, there is disclosed a polarimeter for analyzing a state of polarization of a light beam incident thereon. The polarimeter of the present invention includes first and second variable retarders, wherein at least a selected one of the first and second variable retarders is configured to be progressively and unidirectionally variable through an overall retardance range so as to exhibit a plurality of retardance values. The polarimeter also includes a detector arrangement for detecting at least a spatial portion of the light beam for the plurality of retardance values as the selected one of the first and second variable retarders is progressively and unidirectionally varied through at least a part of the overall retardance range. The polarimeter further includes a control arrangement for causing the selected one of the first and second variable retarders to progressively and unidirectionally vary through the part of the overall retardance range and for extracting the state of polarization based on the spatial portion of the light beam detected at the detector arrangement.
In still another aspect of the invention, another polarimeter for analyzing a state of polarization of a light beam incident thereon is disclosed. The polarimeter of this aspect of the invention includes first and second liquid crystal variable retarders and a detector arrangement for detecting at least a portion of the light beam during a given time period. The polarimeter also includes a control arrangement configured to initially apply a first voltage signal then to apply, for the given time period, a second voltage signal to at least a selected one of the first and second liquid crystal variable retarders. The control arrangement is further configured to extract the state of polarization based on the spatial portion of the light beam detected at the detector arrangement.
In a further aspect of the invention, there is disclosed another method for use in a polarimeter for analyzing a state of polarization of a light beam incident thereon. The polarimeter includes first and second variable retarders and a detector arrangement for taking a measurement of at least a spatial portion of the light beam, wherein the first and second variable retarders are configured to exhibit first and second retardance values, respectively, which first and second retardance values are variable over an overall retardance range. The method includes the steps of directing the light beam through the first and second variable retarders, and varying a selected one of the first and second retardance values over a selected retardance interval. The method further includes the steps of using the detector arrangement to produce a plurality of measurements corresponding to a plurality of measurement points, which plurality of measurement points are incrementally spaced apart across the selected retardance interval, and extracting the state of polarization based on the plurality of measurements.
In a still further aspect of the invention, there is disclosed still another method for use in a polarimeter for analyzing a state of polarization of a light beam incident thereon. The polarimeter includes first and second variable retarders and a detector arrangement, wherein the first and second variable retarders are configured to exhibit first and second retardance values, respectively, which first and second retardance values are variable over an overall retardance range. The method includes the steps of calibrating the polarimeter using a plurality of test input light beams of known polarization states to derive a plurality of basis functions, directing the light beam through the first and second variable retarders, and sweeping a selected one of the first and second retardance values progressively and unidirectionally through at least a part of the overall retardance range. The method further includes the steps of, for a plurality of retardance values that are produced as the selected one of the first and second retardance values is progressively and unidirectionally swept through the part of the overall retardance range, detecting at the detector arrangement at least a portion of the input beam, and extracting the state of polarization by fitting a continuous function to the spatial portion of the light beam detected at the detector arrangement using the plurality of basis functions.